Question

How do you solve the system of equations `x+ y = 8` and `- 2x + 3y = 9`?

Answer 1

`(x,y)to(3,5)`

Explanation:

`"we can use the "color(blue)"substitution method"`

`x+y=8to(1)`

`-2x+3y=9to(2)`

`"from "(1)tox=8-yto(3)`

`"substitute "x=8-y" into equation "(2)`

`-2(8-y)+3y=9`

`-16+2y+3y=9`

`"add 16 to both sides"`

`5y=9+16=25`

`"divide both sides by 5"`

`y=25/5=5`

`"substitute "y=5" into equation "(3)`

`x=8-5=3`

`"point of intersection is "(3,5)`
graph{(y+x-8)(y-2/3x-3)=0 [-10, 10, -5, 5]}